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Eight Degrees of Separation

Author

Listed:
  • Paolo Pin

    (Università Ca’Foscari Venezia)

Abstract
The paper presents a model of network formation where every connected couple gives a contribution to the aggregate payoff, eventually discounted by their distance, and the resources are split between agents through the Myerson value. As equilibrium concept we adopt a refinement of pairwise stability. The only parameters are the number N of agents and a constant cost k for every agent to maintain any single link. This setup shows a wide multiplicity of equilibria, all of them connected, as k ranges over non trivial cases. We are able to show that, for any N, when the equilibrium is a tree (acyclical connected graph), which happens for high k, and there is no decay, the diameter of such a network never exceeds 8 (i.e. there are no two nodes with distance greater than 8). Adopting no decay and studying only trees, we facilitate the analysis but impose worst–case scenarios: we conjecture that the limit of 8 should apply for any possible non–empty equilibrium with any decay function.

Suggested Citation

  • Paolo Pin, 2006. "Eight Degrees of Separation," Working Papers 2006.78, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2006.78
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    References listed on IDEAS

    as
    1. Navarro, Noemí & Perea, Andrés, 2001. "Bargaining in networks and the myerson value," UC3M Working papers. Economics we016121, Universidad Carlos III de Madrid. Departamento de Economía.
    2. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    3. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    4. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    5. Paolo Pin, 2006. "A Model of Myerson-Nash Equilibria in Networks," Lecture Notes in Economics and Mathematical Systems, in: M. Beckmann & H. P. Künzi & G. Fandel & W. Trockel & A. Basile & A. Drexl & H. Dawid & K. Inderfurth (ed.), Artificial Economics, pages 175-188, Springer.
    6. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
    7. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    8. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096, September.
    9. Jackson, Matthew O. & Rogers, Brian W., 2005. "Search in the formation of large networks: How random are socially generated networks?," Working Papers 1216, California Institute of Technology, Division of the Humanities and Social Sciences.
    10. (*), Anne van den Nouweland & Marco Slikker, 2000. "original papers : Network formation models with costs for establishing links," Review of Economic Design, Springer;Society for Economic Design, vol. 5(3), pages 333-362.
    11. Subhadip Chakrabarti & Robert Gilles, 2007. "Network potentials," Review of Economic Design, Springer;Society for Economic Design, vol. 11(1), pages 13-52, June.
    12. Paul Belleflamme & Francis Bloch, 2004. "Market sharing agreements and collusive networks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 387-411, May.
    13. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    14. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521857406, September.
    15. Philippe Mathieu & Bruno Beaufils & Olivier Brandouy, 2005. "Artificial Economics," Post-Print hal-00826572, HAL.
    16. Qin, Cheng-Zhong, 1996. "Endogenous Formation of Cooperation Structures," Journal of Economic Theory, Elsevier, vol. 69(1), pages 218-226, April.
    17. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
    18. Matthew O. Jackson & Brian W. Rogers, 2007. "Meeting Strangers and Friends of Friends: How Random Are Social Networks?," American Economic Review, American Economic Association, vol. 97(3), pages 890-915, June.
    19. Goyal, Sanjeev & Vega-Redondo, Fernando, 2007. "Structural holes in social networks," Journal of Economic Theory, Elsevier, vol. 137(1), pages 460-492, November.
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    Cited by:

    1. Matthew Elliott & Arun Chandrasekhar & Attila Ambrus, 2015. "Social Investments, Informal Risk Sharing, and Inequality," 2015 Meeting Papers 189, Society for Economic Dynamics.
    2. Attila Ambrus & Arun G. Chandrasekhar & Matt Elliott, 2014. "Social Investments, Informal Risk Sharing, and Inequality," NBER Working Papers 20669, National Bureau of Economic Research, Inc.
    3. De Jaegher, K. & Kamphorst, J.J.A., 2015. "Minimal two-way flow networks with small decay," Journal of Economic Behavior & Organization, Elsevier, vol. 109(C), pages 217-239.

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    More about this item

    Keywords

    Network Formation; Myerson Value;

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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